Is the source of odor the padding? Do we need to scrap the padding and replace it with new? Can the padding be saved?

The answer:

In all likelihood the source of the odor is mold. From your description it sounds as if you didn''t do much initially to dry the carpet and pad and consequently the moisture has made it an ideal breeding ground for mold.

It is likely that you will need to replace the carpet and the pad, but more important you need to get the rooms dry.